10.3 Earthquake measurement and intensity scales

Earthquake Measurement and Intensity Scales

Earthquake magnitude tells you how much energy a quake releases, while intensity describes how strongly it's felt at a given location. These are two fundamentally different measurements, and understanding both is key to interpreting earthquake data. This section covers the main scales geologists use and how they locate where earthquakes originate.

Earthquake Magnitude Measurement

Magnitude quantifies the energy released by an earthquake, based on the amplitude of seismic waves recorded on a seismogram. It's a single number assigned to the whole earthquake, no matter where you are when you feel it.

The Richter scale was developed by Charles Richter in 1935 and was the first widely used magnitude scale. It's logarithmic, which means:

• Each whole number increase represents a tenfold increase in wave amplitude (a magnitude 5 quake has waves 10× larger than a magnitude 4)
• Each whole number increase also represents roughly a 32-fold increase in energy released (a magnitude 6 releases about 32× more energy than a magnitude 5)

That second point is the one students often miss. A magnitude 7 doesn't just release a little more energy than a magnitude 6; it releases about 32 times more.

The Richter magnitude is calculated as:

$M_L = \log_{10}(A) - \log_{10}(A_0)$

• $M_L$ = Richter (local) magnitude
• $A$ = maximum amplitude of seismic waves recorded by the seismograph (in millimeters)
• $A_0$ = standard reference amplitude for a baseline earthquake at a distance of 100 km

Limitations of the Richter Scale

The Richter scale works well for small to moderate, nearby earthquakes, but it has real problems beyond that:

• Saturates above ~6.5 magnitude, meaning it underestimates the true energy of large earthquakes. A magnitude 7 and a magnitude 8 might look similar on the Richter scale even though the 8 is far more powerful.
• Tied to a specific instrument (the Wood-Anderson torsion seismograph), which limits its use with modern equipment.
• Inaccurate at great distances because seismic waves weaken (attenuate) as they travel, and the scale doesn't account for this well.

The moment magnitude scale ($M_w$) was developed to fix these problems. Instead of relying on wave amplitude alone, it's based on the seismic moment, which accounts for three physical properties of the fault:

• The area of the fault that ruptured
• The average distance the rock slipped along the fault
• The rigidity (stiffness) of the rock

This makes $M_w$ far more accurate for large earthquakes (above magnitude 7) and for quakes recorded at great distances. It's the scale most seismologists use today for significant earthquakes.

$M_w = \frac{2}{3}\log_{10}(M_0) - 10.7$

where $M_0$ is the seismic moment measured in dyne-cm.

Modified Mercalli Intensity Scale

Unlike magnitude (which is one number for the whole earthquake), intensity varies by location. The Modified Mercalli Intensity (MMI) scale measures how strongly an earthquake is felt and what damage it causes at a specific place. It's qualitative, based on observations and reports rather than instrument readings.

The scale ranges from I (not felt at all) to XII (total destruction):

1. I–III: Not felt to weak shaking. No damage. You might notice hanging objects swinging slightly.
2. IV–VI: Light to strong shaking. Slight to moderate damage, such as cracked plaster, broken dishes, and fallen chimneys.
3. VII–IX: Very strong to violent shaking. Considerable to heavy damage, including collapsed buildings and ground fissures.
4. X–XII: Extreme shaking. Widespread destruction: landslides, bridges destroyed, objects thrown into the air.

A single earthquake will have different MMI values at different locations. Areas near the epicenter typically experience higher intensities, while areas farther away feel less shaking. This makes the MMI scale especially useful for emergency responders, since it shows where damage is worst and helps prioritize relief efforts.

Interpreting Seismograms to Locate Epicenters

A seismogram is the record of ground motion produced by a seismograph. It shows the arrival of different seismic waves, most importantly P-waves (primary, faster) and S-waves (secondary, slower). The epicenter is the point on Earth's surface directly above the hypocenter (also called the focus), which is where the earthquake actually originates underground.

Triangulation method (requires three or more stations):

1. Record the arrival times of P-waves and S-waves at each seismic station.
2. Calculate the time difference between the P-wave and S-wave arrivals at each station. Because P-waves travel faster than S-waves, a larger time gap means the station is farther from the epicenter.
3. Use a travel-time curve or table to convert each time difference into a distance from the epicenter.
4. On a map, draw a circle around each station with a radius equal to its calculated distance.
5. The epicenter is where all three circles intersect (or nearly intersect).

You need a minimum of three stations because a single station only tells you how far away the earthquake is, not which direction. Two stations narrow it down to two possible points. Three stations give you one intersection point.

S-P time method at a single station follows the same logic for calculating distance: measure the S-P time gap, look up the distance on a travel-time curve, and draw a circle. Then repeat at two more stations to complete the triangulation.